Preheat oven to 350°F (175°C). Grease an 8x8 inch baking pan.
In a medium bowl, mix melted butter, sugar, eggs, and vanilla. Add cocoa, flour, salt, and baking powder. Spread half of the batter into the prepared pan.
In another bowl, beat cream cheese, sugar, egg, and vanilla until smooth. Spread over brownie batter in the pan.
Drop remaining brownie batter by spoonfuls over cheesecake layer. Swirl with a knife.
Bake for 35 minutes. Let cool before cutting into squares.